CHM 101
GAGE
Mathematical Models from Scientific Data ANSWERS
Suppose that you suspect that there is a relationship between the volume of a gas sample and its
temperature. To investigate, you collect the following data by changing the temperature and
measuring the resulting volume of the gas.
Temperature (kelvins)
273
283
298
310
318
323
340
358
363
375
1.
Volume (mL)
224
232
247
251
257
266
280
294
299
310
What is the independent variable in this experiment? ______temperature________
Explain.
You are able to set the value of temperature so it does not depend on another variable
while the volume depends on the value for the temperature so therefore it is a dependent
variable.
What variable(s) would you have to control in this situation?
Type of gas, type of container, amount of gas, pressure
2.
From a visual scan of the data decide if the relationship between temperature and volume
is direct or inverse.
direct
If you graphed the data what would you expect to see?
Straight line
3.
On the graphing calculator, enter the independent
variable in L1 and the dependent variable in L2. Display the
graph of the data and decide if your answers to Question 2
are correct.
4.
Determine the mathematical model (equation) for the relationship between temperature
and volume by generating the regression equation for the data set. As you find the
equation, generate the regression coefficient (r2) to determine how well the model fits
the data.
V = 0.839 T – 6.00
where T = temperature (K)
V = volume (mL)
When you use the calculator or Excel to determine a regression equation, the equation
will be displayed in a general format such as y = ax + b. Since you know what the
variables x and y are, and you have the values for “a” and “b”, you must rewrite the
regression equation, substituting the information you have, to arrive at the correctly
formatted equation.
r2 = 0.995
Since r2 is close to the value of 1, most of the variation in the variable y is
explained by changes in x. Therefore, the equation (model) is a good fit
for the data.